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A Novel Numerical Method for Computing Subdivision Depth of Quaternary Schemes

Author

Listed:
  • Aamir Shahzad

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Faheem Khan

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Abdul Ghaffar

    (Department of Mathematics, Ghazi University D G Khan, D G Khan 32200, Pakistan)

  • Shao-Wen Yao

    (School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China)

  • Mustafa Inc

    (Department of Computer Engineering, Biruni University, Istanbul 34096, Turkey
    Department of Mathematics, Science Faculty, Firat University, Elazig 23119,Turkey
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Shafqat Ali

    (Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan)

Abstract

In this paper, an advanced computational technique has been presented to compute the error bounds and subdivision depth of quaternary subdivision schemes. First, the estimation is computed of the error bound between quaternary subdivision limit curves/surfaces and their polygons after k th-level subdivision by using l 0 order of convolution. Secondly, by using the error bounds, the subdivision depth of the quaternary schemes has been computed. Moreover, this technique needs fewer iterations (subdivision depth) to get the optimal error bounds of quaternary subdivision schemes as compared to the existing techniques.

Suggested Citation

  • Aamir Shahzad & Faheem Khan & Abdul Ghaffar & Shao-Wen Yao & Mustafa Inc & Shafqat Ali, 2021. "A Novel Numerical Method for Computing Subdivision Depth of Quaternary Schemes," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:809-:d:532164
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    References listed on IDEAS

    as
    1. Ghulam Mustafa & Faheem Khan, 2009. "A New 4-Point Quaternary Approximating Subdivision Scheme," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-14, June.
    2. Faheem Khan & Ghulam Mustafa & Aamir Shahzad & Dumitru Baleanu & Maysaa M. Al-Qurashi, 2020. "A Computational Method for Subdivision Depth of Ternary Schemes," Mathematics, MDPI, vol. 8(5), pages 1-22, May.
    3. Deng, Chongyang & Jin, Wenbiao & Li, Yajuan & Xu, Huixia, 2017. "A formula for estimating the deviation of a binary interpolatory subdivision curve from its data polygon," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 10-19.
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    Cited by:

    1. Samsul Ariffin Abdul Karim & Faheem Khan & Ghulam Mustafa & Aamir Shahzad & Muhammad Asghar, 2023. "An Efficient Computational Approach for Computing Subdivision Depth of Non-Stationary Binary Subdivision Schemes," Mathematics, MDPI, vol. 11(11), pages 1-12, May.

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    3. Faheem Khan & Ghulam Mustafa & Aamir Shahzad & Dumitru Baleanu & Maysaa M. Al-Qurashi, 2020. "A Computational Method for Subdivision Depth of Ternary Schemes," Mathematics, MDPI, vol. 8(5), pages 1-22, May.

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